Thermodynamics of the Thermal Decomposition of Water by Closed Chemical Cycles Edward L. King University of Colorado, Boulder, CO 80309
+
The thermal decompositionof water as a source of hydrogen is a topic of current interest (1-121, and some of its aspects (13). This have been discussed recently in THIS JOURNAL subject illustrates facets of the thermodynamics of chemical reactions not commonly presented in chemistry textbooks. Of special concern in the present article is the temperature at which the equilibrium constant for a reaction has particular This temperature is value, e.g., K = 1.00 or K = 1.00 X revealed simply in a plot of AH0 versus (ASo - R In K). ReTASo gives an equaarrangement of RT In K = -AHo tion
100.0 k J mol-'I(-20.00 JK-I mol-1 76.58 JK-1 mol-I) = 1767 K. Reaction C is the reverse of reaction A: with AH" = -100.0 kJ mol-' and ASo = -50.00 JK-I mol-', this reaction is represented bv a vector in auadrant 111. In this case K = 1.00 a t 2000 K, andi( > 1.00 at-T < 2000 K. For reactions with &P < 0 and AS: > 0, represented by vectors in quadrant IV, K > 1.00 a t all temperatures. Although the assumption that AC, = 0 is incorrect for most reactions, the value of AC, is small for many reactions, and simplicity is achieved by this assumption. Equilibrium in the thermal decomposition of water vapor
for the temoerature at which the eauilibrium constant hasthe value in qiestion. Under the assumption that AC, = 0, an assumotion that will be em~lovedthrouehout this studv. the values-of AHo and ASo fora chemical reaction are constant, and a particular reaction with a articular value of K is rep- R In K). T ~ s106e P rez~nt&iIly a particular point (A/;'',So of a vector frum the origin tu this point is idpntilied as this temperature by the equation just given. The quantity (ASo R In K), designated AS,, is for a reaction of ideal gases simply the change of entropy for thereaction a t partial pressures of reactants and products which corres~ondto the value of K heing considered (Plots of enthalpy versus entropy for steam) are called Mollier diagrams, fluids (ex., . superheated and they are much used in engineering studies. A use of Mollier diagrams in connection with the thermal decomposition of water, different from the use to be described here, is presented by Knoche and Schubert ( 4 ) J Before considerine the decom~ositionof water. the meanine o i a vector in each quadrant oE the AH", AS, plane will he elurida~ed.Two valut~soi K . K = 1.00 (AS, = ASo J m d K = 1.00 X (AS. = ASo - R In (1.00 x 10'~) = AS" 76.58 JK-' mol-I), are considered in Figures l a and lh. For a reaction designated as reaction A with AHo = +100.0 kJ mol-', AS" = +50.00 JK-1 mol-I, the vector is in quadrant I, and K = 1.00 at T = (100.0 kJ mol-'150.00 JK-I mol-') = 2000 K. For this endothermic reaction, K > 1.00 at T > 2000 K. For a t a lower temperature: this same reaction, K = 1.00 X T = 100.0 kJ m01-~1(50.00JK-I mol-I 76.58 JK-' mol-') = 790.0 K. For a reaction with AHD> 0 and AS0 < 0, the vector, with a negative slope, is in quadrant 11; the value of K is less than 1.00 at all temperatures. An example is reaction B with AHo = +100.0 kJ mol-1, ASo = -20.00 JK-' mol-1. Although K < 1.00 at all temperatures, the equilibrium constant has the value 1.00 X lo-' at a finite temperature: T =
is unfavorable for the formation of hydrogen except at very high temperature; the values of Klatm"2 as a function of temperature are: 298.2 K, 9.0 X 10-41; 1000 K, 8.7 X lo-"; 2000 K, 2.9 X 3000 K, 0.045. The value of this equilibrium constant is 1.00 atm112at -4300 K (14).' (At temperatures a t which the decomposition of water vapor occurs to an appreciable extent, there also are significant amounts of species in addition to HaO(g), Hz(g), and 02(g). At 3000 K, with the total pressure equal to 1.000 a h , approximate partial pressures (Platm) for all of the species are: H ~ 0 ~ 0 . 6 4 Ha, 6; 0.136; 02, 0.045; OH, 0.091; H, 0.058; and 0,0.024 (14).) Current interest in the thermal decom~ositionof water is not focussed on the unassisted process at practically inaccessible temoeratures. but rather is directed a t closed cvcles a~ (15, 1Q2),each member of which of reactions ( ~ o l v clkters
a
+
HnOM = Hn(d
-
I
P
I
+ %0nW
I
I
+
+
Presented in part at the Second Chemical Congress of the North American Continent, Las Vegas, Nevada, August, 1980. Dimensions are included in this equilibrium constant and in ones used later to make unambiguous the standard state for the gases and the pressure units used. May and Rudd (16) use the term "Solvay cluster" tor a series of reactions involving "intermediate chemicals and chemical reactions to bypass an important but unwilling chemical reaction." The Solvay soda ash process for the conversion of sodium chloride plus calcium carbonate into sodium carbonate plus calcium chloride (with A@ = +99 kJ mol-' at 298.2 K) is, like the decomposition of water. a thermodynamically infeasible reaction.
'
4
1.
bl
AHD - A S . plane. a. AH = A*, AS.= ASo, Ac', = 0 Ouadrant I. Reaction A: AHD = t100.0 kJ mol-'. AS'
Figure
The
= +50.00 JK-'
...~
~
~
Reaction 8: AHD = +100.0 kJ mol-'. A 9 = -20.00 JK-' moi-', K < 1.00 at all temperatures. Ouadranf Ill. Reaction C (the reverse of Reaction A): AH' = -100.0 kJ moi-'. ASo = -50.00 JK-' mol-': K = 1.00 at 2000 K. (K > 1.00 at T < Ouadrant 11.
2000 K)
AHD < 0.A 9 > 0: K > 1 atail tempsratures. AH', AS.= A 9 - Rln(l.OOX 10-9. A c ; = 0 Quadrant I Reaction A: K = 1.00 X lo-' at T = 100.0 kJ mol-'l(50.00 OwdrantlV.
b, AH=
mol-' - R In 1.00 X lo-') = 790.0 K. Reaction 8: K = 1.00 X lo-' a1 T = 100.0 kJ m0l-~/(-20.00 JK-' mai-' - R In 1.00 X lor4) = 1767 K. (Above these temperatures. K > 1.00 X Quadrant IV. Reaction C: AH' = -100.0 kJ mol-'; AS, = -50.00 JK-' mot-' - R In 1.00 X lo-" = t26.58 JK-' mol-': K > 1.00 X 1 0 P at all temperatures. JK-'
Volume 58 Number 12 December 1981
975
occurs at lower temperatures; these Solvay clusters have water decompositon as their net result. The simplest imaginable closed cycles involve two steps Oxide Cycle X+H20=XO+Hz
xo = x + l/zOz Hydride Cycle Y + Hz0 = HzY + '120~ H2Y=Hz+Y The intermediate chemicals X and XO or Y and H2Y are not consumed, and in this respect each cycle resembles a common mechanism for catalysis, hut this resemblance is misleading. The decomposition of water a t the lower temperatures in question ( 0 and AS, > 0, can accomplish the decomposition of water a t a temperature below the temperatureat which the unassisted decomposition would occur. The slope of a t least one of the vectors added must he more positive than the slope of
-= lx
Figure 2. AHO versus AS. for the reaction HaO(g1 = H&l+
'/202(9)
The plot is based upon At? = 247.89 kJ mot-', and A 9 = 55.26 JK-' mot-', values appropriate far 1000 K. The slopes of the lines T = AHOlAS. for K/atm"z = 1.00. 1.00 X lo-'. 1.00 X lo@, and 1.00 X are 4490 K. 1880 K. 1190 K. and 870 K. respectively. The wrrecttemperatues fathese values of Kare 4300 K, 1870 K. 1190 K. and 870 K. respectively (14).
I
I1
Each of these reactions is endothermic (at 298.2 K, MI 211.3 kJ mol-l, AH11 = 30.5 kJ mol-') and for reaction I, ASI = -21.8 JK-' mol-I. Thus reaction I is like reaction B in Figure 1; K < 1.00 at all temperatures. The vector for reaction I has a positive slope only for values of K < 0.073, for which AS, > 0 (AS, = -21.8 JK-' mol-1 - 8.315 JK-' mol-I X ln(0.073) = 0). Figure 3 displays the vectors for KI = 1.00 X (AS, = AS, 76.58 JK-I mol-I) andK11= 1.00 atm1i2. These vectors can be added to give the vector which corresponds to the overall reaction having an equilihrium constant x (1.00 atm'I2) = 1.00 X 10W4 K = KI X KII = (1.00 X atml" at a temperature which is the slope of the resultant vector; this temperature is the reciprocal of the weighted average of thc reciprocals of rhl. telnperatures at which reactions I and I1 have the assiynt~dvalues of t hr vquilihrium constants, thr weiehtine " " factors heine the rnlues oi l I I o tor the reactions; that is, at a temperature given by
+
-
-
Even 2000 K is too hiah a temDerature to be achieved in nuclear reaclors, a heat source proposed tor use n thermal decomposltlon of water Wentort (67suggesls 1200 K as an upper lumir achievable In the near future. 976
Journal of Chemical Education
with partial pressures of H20, H*,andO*SUC~ that 6 = 1.00 X 10-'and 6,= 1.00 atm1'2.(For the constructionofthisfigure,me values of b F and A 9 are those for 298.2 K.)
LOO
100
300
AS:/ J K - ' ~ ~
Figure 5. AH' versus A 9 for the reaction
me paints are for me cmp~lnds1. CaO, 2. Li20, 3. % AI2O3, 4. TiO. 5.Zn0, 6. C02(g)(theprodun is Co(g)), 7. wrSOllthe product is NanS03). The vertical line Aso = 102.5JK-' rnol-' is at A 9 = 'Is9(Odg).The dashed line is the
Figure 4. AH' versus A 9 for the reactions-
+
1. 2K(I) H20(g) = K.O(S)
+H
M
11. KnO(s)= 2K(I) + '/202(g) values of AH' and A 9 are lhose for 1000 K (74). the resultant vector, which represents the temperature at which the unassisted reaction occurs. Since no closed cycle consisting of only endothermic reactions is workable for the objective under consideration, let us consider a two-reaction cycle involving an exothermic step. An oxide cycle involving a difficultly decomposable oxide, KzO,~ is such a cycle:
The first of these reactions is exothermic, the second is endothcrmic tat IIXM K. AIII = -104.0 kd mol-',Mli = t351.R kJ mol-I), and the entropy changes (under standard conditions) are such that each reaction has a favorable equilihrium a t temperatures below that for which the water decomposition equilibrium is favorable
and
Figure 4, the plot of AH0versus ASo for this cycle illustrates asecond important point: A closed cycle of reactions with a t least one exothermic reaction may accomplish the decomoosition of water below the temperature a t which the unassisted reaction occurs to the same extent. The wotassium oxide cvcle in which an endothermic reaction occurs at a high temperature and an exuthcrmic reaction orcurc at a low temperature is ;In example of a thermrxhemiral engine, in which some of the energy flowing as heat into the system at the high temperature is converted into chemial energy, the energy of hydrogen and oxygen relative to that of
vector corresponding to the waterdecompositionreaction. The lines radiating horn the origin correspond to T2 = A&/AS;= 1300 K and 1200 K. The lines radiating fromthe point AH' = 241.8 kJ rnol-'. ASo = 44.4 JK-' rnoi-' correspond to TI = A$/As: = 500 K and 400 K. Thus. if a two-reaction oxide cycle wasto have K, = 1 between 400 K and 500 K and K2 = 1 atrn"2 between 1200 K and 1300 K. the point far the oxide would lie in the shaded region. water; the remainder is expelled as heat at the low temperature (15).Although this example illustrates the point being discussed, the temperature required for decomposition of notassium oxide is irnwracticallv hieh. Thii raises the cluestion hf whether a two-reaction o.hdecycle operating between wractical temDeratures is oossible. The inforiation conveied in Figure 4 can equally well be conveved if the vector for reaction 11, the oxide decomposition react& had its origin at the origin of the coordinatesystem. Figure 5 is such a plot with values of AHo and AS" for the decomposition of a number of oxides given as points. The values of ASo for these reactions are close to %SO(Oz(g)) (102.5 JK-1 mol-1 at 298.2 K) because the quantity
{;s.cx,
1
-;S0(X,0,)
I
is close to zero (0 f 20 JK-1 mol-') if both the oxide X,O, and its rtnlucedform ?I arc in a condensed state (or bothare g a s w 117,181.(The dcromposition oigaseous water deviates greatly from this generalization because its reduced Furm H:, has a vtrs small mular entrwv.) also shows lines .. This figure which represent the slopes of vectors corresponding to practical values of temperature, both the low temperature at which the exothermic reaction occurs, T I = 400 K or 500 K and the high temperature at which the endothermic reaction occurs, T2 = 1200 K or 1300 K. The shaded region of this graph defined by the conditions KI = 1.00 at T = 400 K to 500 K and KII = 1.00 atm1I2 at T = 1200 K to 1300 K is far from the coordinates for known oxides. I t seems clear from this graph ~
~
~~~
Thfs cycle nvolving liquid potassium must be viewed as hypothetical oecause the norma boil ng po nt of potassum is 1043.7K. a temperature below ma1at mlch lhe endothem c srep of the cycle could occur. If a cycle involving monoatomic gaseous potassium were considered, each temperature at which K = 1.00 would be lower.
Volume 58 Number 12 December 1981
977
Figure 6. The Three-StepClosed Cycle I. C(s)+ H20(9) =COW + H&) 11. Cob) + 2Fe304(s)= C(s)+ 3Fe20& Ill. 3FezOs(s)= 2FeaOls)+ %0&) The values of A* and ASo used in conshuctlng this graph are those appropr~atefw1000 K: AF( = 135.88kJ mol-' AS; = 143.49JK-' mol-': Afl: = -127.69 k~ mi-'. A S = -227.48 JK-' mol-'; and A d , = 239 70 k~ mol-' and AS;, = 139.25JK-' mol-'
(In.
+
I. C(s) + HzO(g)= CO(g) Hn(g)
11. CO(g) + 2Fe30ds) = C(s) + 3FenOds) 111. 3FezOds) = 2FesOds) + %O&) the individual steps of which do occur a t lower temperatures than the temperature at which the unassisted reaction occurs. The AHo versus ASo graph for this closed cycle, a process studied by Marchetti and de Beni (cited in (7)), is given in Figure 6. If values of AHo and AS" for 1000 K are used in the calculations, the temperature limits for each reaction are: I. K > 1 atm at T > 950 K; 11. K > 1 atm-' at T < 560 K; and 111. K > 1 atml" a t T > 1720 K. The temperature limits mentioned in a presentation of this process (7), 970 K, 520 K, and 1670 K, respectively, are close to those calculated here. Two-reaction hydride cycles are no more promising than two-reaction oxide cycles, hut three-reaction hydride cycles hased upon the reverse Deacon process have been studied (6). One of these involves the chlorides of chromium: I. HnO(g) + CIA4 = 2HCl(g)+ %On(g) 11. 2HCl(g)+ 2CrClz(s)= 2CrCla(s)+ Hdg) 111. 2CrCh(s)= 2CrClz(s)+ Cln(g) Using the values of AHo and AS" for 298.2 K, the temperature 978
Figwe 7. The Three-Step Closed Cycle I. HsOlg) + Cldg) = 2HCl(g) + %02(g) 11. 2HCI(g) + 2CrCI&) = 2CrClds)+ H&) Ill.
that no known oxide will he the basis for a practical two-reaction oxide cycle, a point made in most of the literature already cited. (Quantitative features of the graph would he altered if smaller values of the equilihrium constants were employed or if the experimental points were appropriate for another temperature, hut the conclusion regarding impracticality of a two-reaction oxide cycle would not he changed.) It is possible, however, to meet the critical temperature requirements for the individual reactions with a closed cycle having more than two steps. A two-reaction cycle involving the water-gas reaction, like the silver oxide cycle, involves two endothermic steps, and it cannot advantageously accomplish the decomposition of water. But the water-gas reaction can he made part of a three-reaction closed cycles
Journal of Chemical Education
0
AS./ JK-'~.L-' .Io0
+
2CrCl.(s) = 2CrC12(s) CI2(g)
and A 9 used in constructing this graph are those apThe values of propriate fw 298.2 K: AF( = 57.2 kJ mol-', AS; = 64.4 JK-' mol-'; At( = -148.9 kJ mol-', AS; = -221.3 JK-' mol-': Ah;, = 333.9 kJ mal-', AS;, = 201.2 JK-' mai-'. limits for these reactions are: I. K > 1atm1l2at T > 890 K; 11. K > 1atm-' at T < 670 K, and 111. K > 1atm at T > 1660 K. The vectors representing reactions of this cycle are shown in Figure 7. Many Solvay clusters for the decomposition of water that involve more than three reactions have been proposed, and some of these involve reactions occurring at temperatures where water is a liquid. No new concepts would he introduced hy consideration of these more complex closed cycles. The discussion presented here has focussed upon the use of diagrams that reveal the temperature a t which a reaction has a favorable equilihrium. Provision is made in these diagrams for altering the criterion for a favorable equilihrium by adjusting the value of K in the calculation of AS,: AS, = ASo - R In K, which is the abscissa in the diagram. Other types of graphs have been employed to focus attention upon other aspects of this subject, e.g., entropy versus temperature ( 5 ) , enthalpy versus temperature (71, and free energy versus temperature (16). The author wishes to acknowledge helpful discussion of this subject with Dr. Wesley Jones of the Los Alamos Scientific Laboratory. Literature Cited (1) Funk. J. E., and Reinstmm. R. M..lnd. En#.Chem., P ~ o c ~Design ss ondDeu., 5.131 336 (1966). (21 Funk, J. E., "Proe. Symposium on Non-Famil Chemical Fuels."Amcr. Chem. Soe.. Washington, D.C.. 1972, p. 79. I31 de Beni. G.. and Msrahetti, C., "Pmc. Symposium on Non-Fossil Chemical Fueis: Amer. Chem.Soc.,Washington, D.C., 1972,p. 110. 14) Knoche, K. F.. andSchubert,J., V.D.IForsch.Helf,549,25(1972):(availahIe1E~gIiih translation IONRLAr-25931 from Central Research Library. Oak Ridge National
Laharatory).
(51 Abraham. B. M..sndSchRiner,F.,Scknee,180,959(1973):Ind. E q . Chem.,Fundom., 13.306 (1974). I61 Wentori R. H., sqd Hsnneman. R. E.. Science. 195,311 (1974); Science. 188. 1037 (1975). (7) Chso.8. E..lnd. E n 8 Chsm.,Prod. R e s . D e ~ .13,[21 , 94 (1974).
(31 shimar, R., science, i88,1036 (1875i. 19) Soliman, M. A,. Conger. W. L., Cox, K. E., and Carty, R. H., Seianca, 188, 1037 (19751. I101 Bamberger. C. E..Richardson, D.M., Bredig, M. A.. and Chew, K.. S&nre, 189,716 (1975). Ill) Gregory,D. P., and Pangborn, J. B., Ann. Re", o/Enorgy. I, 279 11976). 1121 Hqenrnull~r,P., Lo Recherche. 8,756 (1977).
(131 ~arnbwger,C. E.. B ~ ~ V I I L, ~B and ~ ~ i,~ h a m l s aD n , M., J. CHBM. EDW. ~5.561 119731. 1141 JANAFThermachornical Tables, Swond Ed.. NSRDS-NBS 37 (1971). I151 Watson, I.D.,and Williarnsun,A.G.,d.C~~~.E~~~.,56,723 (1979). (13) May,D.,snd Rudd,D. F.,Cham.Eng. Sci.,31,59 (19791. (171 Ko1ley.K. K.,andKing. E. G.,US. Bureau of Mines, Bulletin 592.119611. 1131 Brewer,L.,Chem. Rev.,52,1 (1953).
Volume 58
Number 12
December 1981
979
